We first extract backbone features using ResNet50 [1]} and ResNet101 [1]} from conv3\(\_\) x, conv4\(\_\) x and conv5\(\_\) x. This feature extracting scheme results in 3 pyramidal layers. To compose VEM, we stack a series of \(3\times 3 \times 3 \times 3\)  convolutions followed by ReLU and Group Normalization. The coarsest level correaltion map has a size of \(8\times 8 \times 8 \times 8\)  after undergoing VEM. Finer levels, \(p=4\)  and \(p=3\) , have volume embeddings of size \(16\times 16 \times 8 \times 8\)  and \(32 \times 32 \times 8 \times 8\) , respectively. We set the number of heads in VTM as 4. At \(p=5\)  level, we set the depth of VTM as 4 and rest are set to 2. Window size \(M\)  is set to 4 at all levels of VTM. We project the feature maps of query at last layer of level \(p=4, p=3\)  and \(p=2\)  to have channels 64, 32 and 16 from 1024, 512 and 256, respectively. We implemented our work with PyTorch [3]}. We used learning rate of 5e-4. We used augmentation introduced in [4]} for training as shown in Table REF . We adopted early-stopping for all the training, which we picked the model with best validation score. We set the batch size as 16.
